Aims. Following the detection of the fast radio burst FRB150418 by the SUPERB project at the Parkes radio telescope, we aim to search for very-high energy gamma-ray afterglow emission. Methods. Follow-up observations in the very-high energy gamma-ray domain were obtained with the H.E.S.S. imaging atmospheric Cherenkov telescope system within 14.5 h of the radio burst. Results. The obtained 1.4 h of gamma-ray observations are presented and discussed. At the 99% C.L. we obtained an integral upper limit on the gamma-ray flux of Phi(gamma)(E > 350 GeV) < 1.33 x 10(-8) m(-2) s(-1). Differential flux upper limits as function of the photon energy were derived and used to constrain the intrinsic high-energy afterglow emission of FRB 150418. Conclusions. No hints for high-energy afterglow emission of FRB 150418 were found. Taking absorption on the extragalactic background light into account and assuming a distance of z = 0 : 492 based on radio and optical counterpart studies and consistent with the FRB dispersion, we constrain the gamma-ray luminosity at 1 TeV to L < 5 : 1 x 10(47) erg/s at 99% C.L.